Complexity of Left-Ideal, Suffix-Closed and Suffix-Free Regular Languages

A language $L$ over an alphabet $\Sigma$ is suffix-convex if, for any words $x,y,z\in\Sigma^*$, whenever $z$ and $xyz$ are in $L$, then so is $yz$. Suffix-convex languages include three special cases: left-ideal, suffix-closed, and suffix-free languages. We examine complexity properties of these three special classes of suffix-convex regular languages. In particular, we study the quotient/state complexity of boolean operations, product (concatenation), star, and reversal on these languages, as well as the size of their syntactic semigroups, and the quotient complexity of their atoms.Comment: 20 pages, 11 figures, 1 table. arXiv admin note: text overlap with arXiv:1605.0669

Most Complex Non-Returning Regular Languages

A regular language $L$ is non-returning if in the minimal deterministic finite automaton accepting it there are no transitions into the initial state. Eom, Han and Jir\'askov\'a derived upper bounds on the state complexity of boolean operations and Kleene star, and proved that these bounds are tight using two different binary witnesses. They derived upper bounds for concatenation and reversal using three different ternary witnesses. These five witnesses use a total of six different transformations. We show that for each $n\ge 4$ there exists a ternary witness of state complexity $n$ that meets the bound for reversal and that at least three letters are needed to meet this bound. Moreover, the restrictions of this witness to binary alphabets meet the bounds for product, star, and boolean operations. We also derive tight upper bounds on the state complexity of binary operations that take arguments with different alphabets. We prove that the maximal syntactic semigroup of a non-returning language has $(n-1)^n$ elements and requires at least $\binom{n}{2}$ generators. We find the maximal state complexities of atoms of non-returning languages. Finally, we show that there exists a most complex non-returning language that meets the bounds for all these complexity measures.Comment: 22 pages, 6 figure

Quotient Complexity of Regular Languages

The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formal-language terms as the number of distinct quotients of the language, and to call it "quotient complexity". The problem of finding the quotient complexity of a language f(K,L) is considered, where K and L are regular languages and f is a regular operation, for example, union or concatenation. Since quotients can be represented by derivatives, one can find a formula for the typical quotient of f(K,L) in terms of the quotients of K and L. To obtain an upper bound on the number of quotients of f(K,L) all one has to do is count how many such quotients are possible, and this makes automaton constructions unnecessary. The advantages of this point of view are illustrated by many examples. Moreover, new general observations are presented to help in the estimation of the upper bounds on quotient complexity of regular operations

The Magic Number Problem for Subregular Language Families

We investigate the magic number problem, that is, the question whether there exists a minimal n-state nondeterministic finite automaton (NFA) whose equivalent minimal deterministic finite automaton (DFA) has alpha states, for all n and alpha satisfying n less or equal to alpha less or equal to exp(2,n). A number alpha not satisfying this condition is called a magic number (for n). It was shown in [11] that no magic numbers exist for general regular languages, while in [5] trivial and non-trivial magic numbers for unary regular languages were identified. We obtain similar results for automata accepting subregular languages like, for example, combinational languages, star-free, prefix-, suffix-, and infix-closed languages, and prefix-, suffix-, and infix-free languages, showing that there are only trivial magic numbers, when they exist. For finite languages we obtain some partial results showing that certain numbers are non-magic.Comment: In Proceedings DCFS 2010, arXiv:1008.127

A Kleene theorem for polynomial coalgebras

For polynomial functors G, we show how to generalize the classical notion of regular expression to G-coalgebras. We introduce a language of expressions for describing elements of the final G-coalgebra and, analogously to Kleene’s theorem, we show the correspondence between expressions and finite G-coalgebras

Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation

Directed graphs (DG), interpreted as state transition diagrams, are traditionally used to represent finite-state automata (FSA). In the context of formal languages, both FSA and regular expressions (RE) are equivalent in that they accept and generate, respectively, type-3 (regular) languages. Based on our previous work, this paper analyzes effects of graph manipulations on corresponding RE. In this present, starting stage we assume that the DG under consideration contains no cycles. Graph manipulation is performed by deleting or inserting of nodes or arcs. Combined and/or multiple application of these basic operators enable a great variety of transformations of DG (and corresponding RE) that can be seen as mutants of the original DG (and corresponding RE). DG are popular for modeling complex systems; however they easily become intractable if the system under consideration is complex and/or large. In such situations, we propose to switch to corresponding RE in order to benefit from their compact format for modeling and algebraic operations for analysis. The results of the study are of great potential interest to mutation testing

Aceite de germen de trigo obtenido mediante extracción con dióxido de carbono supercrítico con etanol: Composición en ácidos grasos

In this work, supercritical fluid extraction (SFE) using CO2 with ethanol as entrainer was performed at a temperature of 40 oC under a pressure of 21 MPa. For comparison, a similar extraction without the entrainer was carried out. The extraction yield of wheat germ using supercritical CO2 with ethanol was slightly higher (10.7 wt%) than that of extraction without the entrainer (9.9 wt%). Fractions of SFE extracts were collected separately during the experiments and the composition of fatty acids in each fraction was analyzed. The SFE extracted oils were rich (63.4-71.3%) in the most valuable polyunsaturated fatty acids (PUFA) and their content in all collected fractions was approximately constant. Similar PUFA contents were found in the reference samples of oils extracted by n-hexane (66.2-67.0%), while the commercial cold-pressed oil contained significantly less PUFA (60.2%). These results show a higher nutritional value of the oil obtained by extraction with supercritical CO2 than cold pressed oil which is generally considered to be very valuable.En este trabajo, la extracción con fluidos supercríticos (SFE) usando CO2 con etanol como agente de arrastre se realizó a 40 °C bajo una presión de 21 MPa. Se ha llevado a cabo la comparación con una extracción similar sin agente de arrastre. El rendimiento de la extracción de germen de trigo usando CO2 supercrítico con etanol fue ligeramente mayor (10,7% en peso) que la de extracción sin agente de arrastre (9,9% en peso). Se recogieron por separado fracciones de extractos SFE durante los experimentos y se analizó la composición de ácidos grasos en cada fracción. Los aceites extraídos mediante SFE eran ricos en los ácidos grasos poliinsaturados más valiosos (63,4-71,3%), (PUFA) y su contenido en todas las fracciones recogidas fue aproximadamente constante. Un contenido similar de PUFA fueron encontrados en muestras de referencia de los aceites extraídos con n-hexano (66,2-67,0%), mientras que el aceite prensado en frío comercial contenía significativamente menos PUFA (60,2%). Estos resultados muestran un mayor valor nutritivo del aceite obtenido por extracción con CO2 supercrítico que el aceite prensado en frío que generalmente se considera que es muy valioso

Change Actions: Models of Generalised Differentiation

Cai et al. have recently proposed change structures as a semantic framework for incremental computation. We generalise change structures to arbitrary cartesian categories and propose the notion of change action model as a categorical model for (higher-order) generalised differentiation. Change action models naturally arise from many geometric and computational settings, such as (generalised) cartesian differential categories, group models of discrete calculus, and Kleene algebra of regular expressions. We show how to build canonical change action models on arbitrary cartesian categories, reminiscent of the F\`aa di Bruno construction

Identifying and dating the destruction of hydrocarbon reservoirs using secondary chemical remanent magnetization

Destructive processes are thought to be common in pre‐Cenozoic oil‐gas reservoirs. The timing, mechanism, and even identification of these processes, however, are difficult to clearly characterize, which obscures the evolution of such systems and the assessment of oil and gas reserves. Here, we reveal a new link between secondary chemical remanent magnetization acquisition and tectonically driven destruction of hydrocarbon reservoirs, which can be used to date the destructive processes and identify their tectonic controls. We performed a detailed paleomagnetic analysis of rocks from a typical destroyed reservoir (Majiang reservoir, China) and combined these data with scanning electronic microscope imaging and strontium isotope, total organic carbon, and clay analysis. We found that the Late Triassic syntilting secondary chemical remanent magnetizations of source and reservoir rocks resulted from the destructive processes driven by the Indosinian orogeny. We therefore argue that palaeomagnetic methods can be used to constrain destructive events within hydrocarbon reservoirs worldwide